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Mathematical Logic = Exercises and Solutions /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematical Logic/ by Laszlo Csirmaz, Zalán Gyenis.
其他題名:	Exercises and Solutions /
作者:	Csirmaz, Laszlo.
其他作者:	Gyenis, Zalán.
面頁冊數:	VIII, 319 p. 5 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Model Theory. -
電子資源:	https://doi.org/10.1007/978-3-030-79010-3
ISBN:	9783030790103

Mathematical Logic = Exercises and Solutions /
Csirmaz, Laszlo.

Mathematical LogicExercises and Solutions /[electronic resource] :by Laszlo Csirmaz, Zalán Gyenis. - 1st ed. 2022. - VIII, 319 p. 5 illus.online resource. - Problem Books in Mathematics,2197-8506. - Problem Books in Mathematics,.

Chapter 1 - Special Set Systems -- Chapter 2 - Games and Voting -- Chapter 3 - Formal languages and automata -- Chapter 4 - Recursion Theory -- Chapter 5 - Propositional Calculus -- Chapter 6 - First-order logic -- Chapter 7 - Fundamental Theorems -- Chapter 8 - Elementary Equivalence -- Chapter 9 - Ultraproducts -- Chapter 10 - Arithmetic -- Chapter 11 - Selected Applications -- Chapter 12 - Solutions.

This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene’s theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht– Fraïssé game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson’s theory, Peano’s axiom system, and Gödel’s incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style and topics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including Gödel’s famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.

ISBN: 9783030790103

Standard No.: 10.1007/978-3-030-79010-3doiSubjects--Topical Terms:

1394048
Model Theory.

LC Class. No.: QA8.9-10.3

Dewey Class. No.: 511.3

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